It is a legal move to amphib Cauc on G1 with the SZ 13 trans.
Looking at the board, it would be 1 inf, 1 arm, 1 bomb vs. 4 inf and the AA gun.
You have noted that this attack will leave the “back door” open… I think the bigger problem with this attack is that you are basically ceding Africa to the Allies. In my group, we non-combat the SZ 13 trans to the Libya SZ, where it is safe from the RAF in Egypt, landing the inf and arm in Libya.
With the G1 Cauc attack, the German transport is nearly guaranteed to die to the RAF fighter in Egypt. Without this transport, and if you re-amphib Cauc with the Italians, the Axis could find themselves out-of-Africa within 3-4 turns. (Our groups standard UK2 move is to land in Morocco with a few transports, followed by the Americans)
Due to the importance of the transport, I personally would only make 2 moves in the Med. Both are designed to avoid getting killed by the RAF fighter. Either- amphib Egypt with everything, and hope to kill the fighter. Or do the non-combat drop off in Libya, using the Italian Navy as a screen.